Daniel is 8 years older than Gabriela. Ten years ago, Daniel was 5 times as old as Gabriela. How old is Gabriela now?
Answer: We can use the given information to write down two equations that describe the ages of Daniel and Gabriela. Let Daniel's current age be $d$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $d = g + 8$ Ten years ago, Daniel was $d - 10$ years old, and Gabriela was $g - 10$ years old. The information in the second sentence can be expressed in the following equation: $d - 10 = 5(g - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to use our first equation for $d$ and substitute it into our second equation. Our first equation is: $d = g + 8$ . Substituting this into our second equation, we get the equation: $(g + 8)$ $-$ $10 = 5(g - 10)$ which combines the information about $g$ from both of our original equations. Simplifying both sides of this equation, we get: $g - 2 = 5 g - 50$ Solving for $g$ , we get: $4 g = 48$ $g = 12$.